NeurIPS 2025 论文列表

We study online adversarial regression with convex losses against a rich class of continuous yet highly irregular competitor functions,% prediction rules, modeled by Besov spaces $B_{pq}^s$ with general parameters $1 \leq p,q \leq \infty$ and smoothness $s > \tfrac{d}{p}$. We introduce an adaptive wavelet-based algorithm that performs sequential prediction without prior knowledge of $(s,p,q)$, and establish minimax-optimal regret bounds against any comparator in $B_{pq}^s$. We further design a locally adaptive extension capable of sequentially adapting to spatially inhomogeneous smoothness. This adaptive mechanism adjusts the resolution of the predictions over both time and space, yielding refined regret bounds in terms of local regularity. Consequently, in heterogeneous environments, our adaptive guarantees can significantly surpass those obtained by standard global methods.

Safety is a fundamental challenge in reinforcement learning (RL), particularly in real-world applications such as autonomous driving, robotics, and healthcare. To address this, Constrained Markov Decision Processes (CMDPs) are commonly used to enforce safety constraints while optimizing performance. However, existing methods often suffer from significant safety violations or require a high sample complexity to generate near-optimal policies. We address two settings: relaxed feasibility, where small violations are allowed, and strict feasibility, where no violation is allowed. We propose a model-based primal-dual algorithm that balances regret and bounded constraint violations, drawing on techniques from online RL and constrained optimization. For relaxed feasibility, we prove that our algorithm returns an $\varepsilon$-optimal policy with $\varepsilon$-bounded violation with arbitrarily high probability, requiring $\tilde{O}\left(\frac{SAH^3}{\varepsilon^2}\right)$ learning episodes, matching the lower bound for unconstrained MDPs. For strict feasibility, we prove that our algorithm returns an $\varepsilon$-optimal policy with zero violation with arbitrarily high probability, requiring $\tilde{O}\left(\frac{SAH^5}{\varepsilon^2\zeta^2}\right)$ learning episodes, where $\zeta$ is the problem-dependent Slater constant characterizing the size of the feasible region. This result matches the lower bound for learning CMDPs with access to a generative model. Episodic tabular CMDPs serve as a crucial benchmark for safe RL, providing a structured environment for theoretical analysis and algorithmic validation. Our results demonstrate that learning CMDPs in an online setting is as easy as learning with a generative model and is no more challenging than learning unconstrained MDPs when small violations are allowed.

The multi-armed bandit (MAB) is a fundamental online decision-making framework that has been extensively studied over the past two decades. To mitigate the high cost and slow convergence of purely online learning, modern MAB approaches have explored _hybrid_ paradigms that leverage offline data to warm-start online learning. However, existing approaches face a significant limitation by assuming that the offline and online data are homogeneous—they share the same feedback structure and are drawn from the same underlying distribution. This assumption is often violated in practice, where offline data often originate from diverse sources and evolving environments, resulting in feedback heterogeneity and distributional shifts. In this work, we tackle the challenge of learning across this offline-online gap by developing a general hybrid bandit framework that incorporates heterogeneous offline data to improve online performance. We study two hybrid settings: (1) using reward-based offline data to accelerate online learning in preference-based bandits (i.e., dueling bandits), and (2) using preference-based offline data to improve online standard MAB algorithms. For both settings, we design novel algorithms and derive tight regret bounds that match or improve upon existing benchmarks despite heterogeneity. Empirical evaluations on both synthetic and real-world datasets show that our proposed methods significantly outperform baseline algorithms.

We study the problem of multiclass learning with bandit feedback in both the i.i.d. batch and adversarial online models. In the *uniform* learning framework, it is well known that no hypothesis class $\mathcal{H}$ is learnable in either model when the effective number of labels is unbounded. In contrast, within the *universal* learning framework, recent works by (Hanneke et al., 2025b) and (Hanneke et al., 2025a) have established surprising exact equivalences between learnability under bandit feedback and full supervision in both the i.i.d. batch and adversarial online models, respectively. This raises a natural question: What happens in the *non-uniform* learning framework, which lies between the uniform and universal learning frameworks? Our contributions are twofold: (1) We provide a combinatorial characterization of learnable hypothesis classes in both models, in the realizable and agnostic settings, within the non-uniform learning framework. Notably, this includes elementary and natural hypothesis classes, such as a countably infinite collection of constant functions over some domain that is learnable in both models. (2) We construct a hypothesis class that is non-uniformly learnable under full supervision in the adversarial online model (and thus also in the i.i.d. batch model), but not non-uniformly learnable under bandit feedback in the i.i.d. batch model (and thus also not in the adversarial online model). This serves as our main novel technical contribution that reveals a fundamental distinction between the non-uniform and universal learning frameworks.

We propose a new method for the problem of controlling linear dynamical systems under partial observation and adversarial disturbances. Our new algorithm, Double Spectral Control (DSC), matches the best known regret guarantees while exponentially improving runtime complexity over previous approaches in its dependence on the system's stability margin. Our key innovation is a two-level spectral approximation strategy, leveraging double convolution with a universal basis of spectral filters, enabling efficient and accurate learning of the best linear dynamical controllers.

We study contextual online pricing with biased offline data. For the scalar price elasticity case, we identify the instance-dependent quantity $\delta^2$ that measures how far the offline data lies from the (unknown) online optimum. We show that the time length $T$, bias bound $V$, size $N$ and dispersion $\lambda_{\min}(\hat{\Sigma})$ of the offline data, and $\delta^2$ jointly determine the statistical complexity. An Optimism‑in‑the‑Face‑of‑Uncertainty (OFU) policy achieves a minimax-optimal, instance-dependent regret bound $\tilde{\mathcal{O}}\big(d\sqrt{T} \wedge (V^2T + \frac{dT }{\lambda_{\min}(\hat{\Sigma}) + (N \wedge T) \delta^2})\big)$. For general price elasticity, we establish a worst‑case, minimax-optimal rate $\tilde{\mathcal{O}}\big(d\sqrt{T} \wedge (V^2T + \frac{dT }{\lambda_{\min}(\hat{\Sigma})})\big)$ and provide a generalized OFU algorithm that attains it. When the bias bound $V$ is unknown, we design a robust variant that always guarantees sub‑linear regret and strictly improves on purely online methods whenever the exact bias is small. These results deliver the first tight regret guarantees for contextual pricing in the presence of biased offline data. Our techniques also transfer verbatim to stochastic linear bandits with biased offline data, yielding analogous bounds.

We study the problem of contextual combinatorial semi-bandits, where input contexts are mapped into subsets of size $m$ of a collection of $K$ possible actions. In each round of the interaction, the learner observes feedback consisting of the realized reward of the predicted actions. Motivated by prototypical applications of contextual bandits, we focus on the $s$-sparse regime where we assume that the sum of rewards is bounded by some value $s \ll K$. For example, in recommendation systems the number of products purchased by any customer is significantly smaller than the total number of available products. Our main result is for the $(\varepsilon,\delta)$-PAC variant of the problem for which we design an algorithm that returns an $\varepsilon$-optimal policy with high probability using a sample complexity of $\widetilde{O}\big( (\mathrm{poly}(K/m) + sm / \varepsilon^2) \log (|\Pi|/\delta) \big)$ where $\Pi$ is the underlying (finite) class and $s$ is the sparsity parameter. This bound improves upon known bounds for combinatorial semi-bandits whenever $s \ll K$, and in the regime where $s = O(1)$, the leading terms in our bound match the corresponding full-information rates, implying that bandit feedback essentially comes at no cost. Our PAC learning algorithm is also computationally efficient given access to an ERM oracle for $\Pi$. Our framework generalizes the list multiclass classification problem with bandit feedback, which can be seen as a special case with binary reward vectors. In the special case of single-label classification corresponding to $s=m=1$, we prove an $O \big((K^7 + 1/\varepsilon^2)\log (|\mathcal{H}|/\delta)\big)$ sample complexity bound for a finite hypothesis class $\mathcal{H}$, which improves upon recent results in this scenario. Additionally, we consider the regret minimization setting where data can be generated adversarially, and establish a regret bound of $\widetilde O(|\Pi| + \sqrt{smT \log |\Pi|})$, extending the result of Erez et al. ('24) who consider the simpler single label classification setting.

We propose a framework for hypothesis testing on conditional probability distributions, which we then use to construct *statistical tests of functionals of conditional distributions*. These tests identify the inputs where the functionals differ with high probability, and include tests of conditional moments or two-sample tests. Our key idea is to transform confidence bounds of a learning method into a test of conditional expectations. We instantiate this principle for kernel ridge regression (KRR) with subgaussian noise. An intermediate data embedding then enables more general tests — including *conditional two-sample tests* — via kernel mean embeddings of distributions. To have guarantees in this setting, we generalize existing pointwise-in-time or time-uniform confidence bounds for KRR to previously-inaccessible yet essential cases such as infinite-dimensional outputs with non-trace-class kernels. These bounds also circumvent the need for independent data, allowing for instance online sampling. To make our tests readily applicable in practice, we introduce bootstrapping schemes leveraging the parametric form of testing thresholds identified in theory to avoid tuning inaccessible parameters. We illustrate the tests on examples, including one in process monitoring and comparison of dynamical systems. Overall, our results establish a comprehensive foundation for conditional testing on functionals, from theoretical guarantees to an algorithmic implementation, and advance the state of the art on confidence bounds for vector-valued least squares estimation.

In the adaptive sampling model of online learning, future prediction tasks can be arbitrarily dependent on the past. Every round, an adversary selects an instance to test the learner. After the learner makes a prediction, a noisy label is drawn from an underlying conditional label distribution and is revealed to both learner and adversary. A learner is consistent if it eventually performs no worse than the Bayes predictor. We study the $k_n$-nearest neighbor learner within this setting. In the worst-case, the learner will fail because an adaptive process can generate spurious patterns out of noise. However, under the mild smoothing assumption that the process generating the instances is uniformly absolutely continuous and that choice of $(k_n)_n$ is reasonable, the $k_n$-nearest neighbor rule is online consistent.

Given a task and a set of steps composing it, Video Step Grounding (VSG) aims to detect which steps are performed in a video. Standard approaches for this task require a labeled training set (e.g., with step-level annotations or narrations), which may be costly to collect. Moreover, they process the full video offline, limiting their applications for scenarios requiring online decisions. Thus, in this work, we explore how to perform VSG online and without training. We achieve this by exploiting the zero-shot capabilities of recent Large Multimodal Models (LMMs). In particular, we use LMMs to predict the step associated with a restricted set of frames, without access to the whole video. We show that this online strategy without task-specific tuning outperforms offline and training-based models. Motivated by this finding, we develop Bayesian Grounding with Large Multimodal Models (BaGLM), further injecting knowledge of past frames into the LMM-based predictions. BaGLM exploits Bayesian filtering principles, modeling step transitions via (i) a dependency matrix extracted through large language models and (ii) an estimation of step progress. Experiments on three datasets show superior performance of BaGLM over state-of-the-art training-based offline methods.

We revisit the problem of private online learning, in which a learner receives a sequence of $T$ data points and has to respond at each time-step a hypothesis. It is required that the entire stream of output hypotheses should satisfy differential privacy. Prior work of Golowich and Livni [2021] established that every concept class $\mathcal{H}$ with finite Littlestone dimension $d$ is privately online learnable in the realizable setting. In particular, they proposed an algorithm that achieves an $O_{d}(\log T)$ mistake bound against an oblivious adversary. However, their approach yields a suboptimal $\tilde{O}\_{d}(\sqrt{T})$ bound against an adaptive adversary. In this work, we present a new algorithm with a mistake bound of $O_{d}(\log T)$ against an adaptive adversary, closing this gap. We further investigate the problem in the agnostic setting, which is more general than the realizable setting as it does not impose any assumptions on the data. We give an algorithm that obtains a sublinear regret of $\tilde{O}_d(\sqrt{T})$ for generic Littlestone classes, demonstrating that they are also privately online learnable in the agnostic setting.

In non-clairvoyant scheduling, the goal is to minimize the total job completion time without prior knowledge of individual job processing times. This classical online optimization problem has recently gained attention through the framework of learning-augmented algorithms. We introduce a natural setting in which the scheduler receives continuous feedback in the form of progress bars—estimates of the fraction of each job completed over time. We design new algorithms for both adversarial and stochastic progress bars and prove strong competitive bounds. Our results in the adversarial case surprisingly induce improved guarantees for learning-augmented scheduling with job size predictions. We also introduce a general method for combining scheduling algorithms, yielding further insights in scheduling with predictions. Finally, we propose a stochastic model of progress bars as a more optimistic alternative to conventional worst-case models, and present an asymptotically optimal scheduling algorithm in this setting.

We provide an algorithm with regret $O(C d \log \log T)$ for contextual pricing with $C$ corrupted rounds, improving over the previous bound of $O(d^3 C \log^2(T))$ of Krishnamurthy et al. The result is based on a reduction that calls the uncorrupted algorithm as a black-box, unlike the previous approach that modifies the inner workings of the uncorrupted algorithm. As a result, it leads to a conceptually simpler algorithm. Finally, we provide a lower bound ruling out a $O(C + d\log \log T)$ algorithm. This shows that robustifying contextual pricing is harder than robustifying contextual search with $\epsilon$-ball losses, for which it is possible to design algorithms where corruptions add only an extra additive term $C$ to the regret.

Increasing demand for Large Language Models (LLMs) services imposes substantial deployment and computation costs on providers. LLM routing offers a cost-efficient solution by directing queries to the optimal LLM based on model and query features. However, existing works primarily focus on offline scenarios and struggle to adapt to online settings with high query volume and constrained token budgets. In this work, we introduce the first training-free algorithm for online routing scenarios. Our algorithm leverages approximate nearest neighbor search to efficiently estimate the features of queries and performs a one-time optimization over a small set of initial queries to learn a set of routing weights that guide future routing. We provide a theoretical guarantee that the algorithm achieves a competitive ratio of $1 - o(1)$ under natural assumptions, which is further validated by extensive experiments across 3 benchmark datasets and 8 baselines, showing an average improvement of 3.55$\times$ in performance, 1.85$\times$ in cost efficiency, and nearly 4.25$\times$ in throughput. Our code is available at https://github.com/fzwark/PORT.

Large language models (LLMs) have facilitated a wide range of applications with distinct service-level objectives (SLOs), from latency-sensitive online tasks like interactive chatbots to throughput-oriented offline workloads like data synthesis. The existing deployment model, which dedicates machines to each workload, simplifies SLO management but often leads to poor resource utilization. This paper introduces HyGen, an interference-aware LLM serving system that enables efficient co-location of online and offline workloads while preserving SLOs. HyGen incorporates two key innovations: (1) performance control mechanisms, including a latency predictor to estimate batch execution time and an SLO-aware profiler to quantify latency interference, and (2) SLO-aware offline scheduling policies that maximize serving throughput and prevent starvation. Our evaluation on production workloads shows that HyGen achieves up to 3.9-5.8× throughput gains over online and hybrid serving baselines, while ensuring latency SLOs. The code of HyGen is publicly available at https://github.com/UIUC-MLSys/HyGen.

Online bipartite matching is a fundamental problem in online optimization, extensively studied both in its integral and fractional forms due to its theoretical significance and practical applications, such as online advertising and resource allocation. Motivated by recent progress in learning-augmented algorithms, we study online bipartite fractional matching when the algorithm is given advice in the form of a suggested matching in each iteration. We develop algorithms for both the vertex-weighted and unweighted variants that provably dominate the naive ``coin flip'' strategy of randomly choosing between the advice-following and advice-free algorithms. Moreover, our algorithm for the vertex-weighted setting extends to the AdWords problem under the small bids assumption, yielding a significant improvement over the seminal work of Mahdian, Nazerzadeh, and Saberi (EC 2007, TALG 2012). Complementing our positive results, we establish a hardness bound on the robustness-consistency tradeoff that is attainable by any algorithm. We empirically validate our algorithms through experiments on synthetic and real-world data.

We revisit the contextual cascading bandit, where a learning agent recommends an ordered list (\emph{cascade}) of items, and a user scans the list sequentially, stopping at the first attractive item. Although cascading bandits underpin various applications including recommender systems and search engines, the role of the cascade length $K$ in shaping regret has remained unclear. Contrary to prior results that regret grows with $K$, we prove that regret actually \emph{decreases} once $K$ is large enough. Leveraging this insight, we design a new upper-confidence-bound algorithm built on online mirror descent that attains the sharpest known regret upper bound, $\tilde{\mathcal{O}}\bigl(\min \lbrace K\bar{p}^{K-1}, 1 \rbrace d \sqrt{T}\bigr)$ for contextual cascading bandits. To complement this new regret upper bound, we provide a nearly matching lower bound of $\Omega \bigl(\min \lbrace K\underline{p}^{K-1}, 1 \rbrace d \sqrt{T}\bigr)$, where $0 \leq \underline{p} \leq \bar{p} < 1$. Together, these results fully characterize how regret truly scales with $K$, thereby closing the theoretical gap for contextual cascading bandits. Finally, comprehensive experiments validate our theoretical results and show the effectiveness of our proposed method.

Understanding when learning is possible is a fundamental task in the theory of machine learning. However, many characterizations known from the literature deal with abstract learning as a mathematical object and ignore the crucial question: when can learning be implemented as a computer program? We address this question for universal online learning, a generalist theoretical model of online binary classification, recently characterized by Bousquet et al. (STOC 2021). In this model, there is no hypothesis fixed in advance; instead, Adversary—playing the role of Nature—can change their mind as long as local consistency with the given class of hypotheses is maintained. We require Learner to achieve a finite number of mistakes while using a strategy that can be implemented as a computer program. We show that universal online learning does not imply computable universal online learning, even if the class of hypotheses is relatively easy from a computability-theoretic perspective. We then study the agnostic variant of computable universal online learning and provide an exact characterization of classes that are learnable in this sense. We also consider a variant of proper universal online learning and show exactly when it is possible. Together, our results give a more realistic perspective on the existing theory of online binary classification and the related problem of inductive inference.

Given a collection of monotone submodular functions, the goal of Two-Stage Submodular Maximization (2SSM) (Balkanski et al. 2016) is to restrict the ground set so an objective selected u.a.r. from the collection attains a high maximal value, on average, when optimized over the restricted ground set. We introduce the Online Two-Stage Submodular Maximization (O2SSM) problem, in which the submodular objectives are revealed in an online fashion. We study this problem for weighted threshold potential functions, a large and important subclass of monotone submodular functions that includes influence maximization, data summarization, and facility location, to name a few. We design an algorithm that achieves sublinear $(1 - 1/e)^2$-regret under general matroid constraints and $(1 - 1/e)(1-e^{-k}k^k/k!)$-regret in the case of uniform matroids of rank $k$; the latter also yields a state-of-the-art bound for the (offline) 2SSM problem. We empirically validate the performance of our online algorithm with experiments on real datasets.